Subgroups — C₃⋊D₃×#436 #11859254

Order 1152.

1656 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₄×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₃²×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	#10592827	C₂	1	2	yes	maximal, complemented
5	#10592711	C₂	1	1	yes	maximal, characteristic, complemented
6	#10592537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃⋊D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592428	C₂	1	2	yes	maximal, complemented
9	C₃⋊D₃×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
10	#10592387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×#436	—	3	4	no	maximal
13	C₂×D₄×C₃⋊D₃	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₃⋊D₃	C₂²	1	2	yes	—
15	C₂×C₃²×M₁₆	C₂²	1	2	yes	complemented
16	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
17	D₄×C₃⋊Dic₃	C₄	1	1	yes	characteristic
18	C₄×#638	C₂²	1	2	yes	—
19	C₂×#3748	C₂²	1	2	yes	complemented
20	M₁₆×C₃⋊D₃	—	2	8	no	—
21	C₂×#3743	C₂²	1	2	yes	complemented
22	C₂×#3743	C₂²	1	2	yes	complemented
23	C₂×C₈×C₃⋊D₃	C₂²	1	2	yes	—
24	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
25	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
26	#64102	C₄	1	1	yes	characteristic
27	C₄⋊C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
28	#64090	C₄	1	2	yes	—
29	C₂²⋊C₄×C₃⋊D₃	C₄	1	2	yes	—
30	C₄×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
31	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
32	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
35	#63657	C₂²	1	2	yes	complemented
36	#63647	C₂²	1	2	yes	complemented
37	#63647	C₂²	1	2	yes	complemented
38	#63641	C₂²	1	2	yes	complemented
39	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
41	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₃×M₁₆	—	3	8	no	—
44	C₄×D₃×D₄	—	3	4	no	—
45	C₃×#436	D₃	1	4	yes	complemented
46	#5128	—	3	8	no	—
47	#5012	—	3	4	no	—
48	#4838	—	3	4	no	—
49	D₃×C₄⋊C₈	—	3	4	no	—
50	#4729	—	3	8	no	—
51	D₃×C₂²⋊C₈	—	3	8	no	—
52	#4688	—	3	4	no	—
53	C₄×D₃×C₈	—	3	4	no	—
54	C₂³×C₃⋊D₃	C₂×C₄	1	2	yes	—
55	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃²×C₄	C₂³	1	2	yes	—
57	C₂×#638	C₂×C₄	1	2	yes	—
58	C₂²×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
59	D₄×C₃⋊D₃	—	2	4	no	—
60	C₂×C₄⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₃⋊D₃	—	2	4	no	—
62	C₂×C₄×C₃⋊D₃	—	2	4	no	—
63	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
65	C₂×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×C₃⋊D₃	C₂³	1	2	yes	—
68	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
69	C₃²×M₁₆	—	2	4	no	—
70	C₂×C₃²×C₈	C₂³	1	2	yes	—
71	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₃²×C₄²	C₂³	1	1	yes	characteristic
76	#3757	C₂×C₄	1	2	yes	—
77	#3752	C₂×C₄	1	2	yes	—
78	#3752	C₂×C₄	1	2	yes	—
79	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
80	#3750	C₂×C₄	1	2	yes	—
81	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
84	#3748	—	2	4	no	—
85	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
86	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
87	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
88	#3743	—	2	4	no	—
89	#3743	—	2	4	no	—
90	C₈×C₃⋊D₃	—	2	4	no	—
91	C₈×C₃⋊D₃	—	2	2	no	—
92	C₈×C₃⋊D₃	D₄	1	4	yes	complemented
93	C₂×#436	—	9	1	no	Sylow
94	C₂×D₃×D₄	—	3	4	no	—
95	C₂²×C₄×D₃	—	3	8	no	—
96	C₂×C₃×M₁₆	C₂×D₃	1	8	yes	complemented
97	C₃×C₄×D₄	C₂×D₃	1	4	yes	—
98	D₄×Dic₃	—	3	4	no	—
99	C₄×#67	—	3	8	no	—
100	C₂×#208	—	3	8	no	—
101	D₃×M₁₆	—	6	32	no	—
102	C₂×ΓL(1,𝔽₂₅)	—	3	8	no	—
103	C₂×ΓL(1,𝔽₂₅)	—	3	8	no	—
104	C₂×D₃×C₈	—	3	4	no	—
105	C₂×D₃×C₈	—	3	4	no	—
106	C₂×D₃×C₈	—	3	8	no	—
107	#893	—	3	4	no	—
108	D₃×C₄⋊C₄	—	3	4	no	—
109	#67⋊C₄	—	3	8	no	—
110	D₃×C₂²⋊C₄	—	3	8	no	—
111	C₄×D₁₂	—	3	4	no	—
112	C₄²×D₃	—	3	4	no	—
113	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
114	C₃×C₂²⋊C₈	C₂×D₃	1	8	yes	complemented
115	C₃×C₄×C₈	C₂×D₃	1	4	yes	complemented
116	#830	—	3	8	no	—
117	(C₂×D₃)⋊C₈	—	3	8	no	—
118	(C₂×D₃)⋊C₈	—	3	8	no	—
119	Dic₃⋊C₈	—	3	8	no	—
120	C₈×Dic₃	—	3	4	no	—
121	C₈×Dic₃	—	3	4	no	—
122	C₄⋊(C₃⋊C₈)	—	3	4	no	—
123	C₄×C₃⋊C₈	—	3	4	no	—
124	C₂³×C₃²	C₂²×C₄	1	2	yes	—
125	C₂²×C₃⋊D₃	—	2	4	no	—
126	C₂²×C₃⋊D₃	—	2	4	no	—
127	C₂²×C₃⋊D₃	—	2	4	no	—
128	C₂²×C₃⋊D₃	C₂²×C₄	1	2	yes	—
129	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
130	C₃²×D₄	—	2	2	no	—
131	C₂×C₃²×C₄	—	2	2	no	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
135	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
137	#638	—	2	4	no	—
138	C₂×C₃⋊Dic₃	—	2	4	no	—
139	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃⋊Dic₃	C₂²×C₄	1	2	yes	—
141	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊(C₃⋊D₃)	—	2	2	no	—
144	C₄×C₃⋊D₃	—	2	4	no	—
145	C₄×C₃⋊D₃	—	2	2	no	—
146	C₄×C₃⋊D₃	—	2	2	no	—
147	C₄×C₃⋊D₃	—	2	2	no	—
148	C₄×C₃⋊D₃	—	2	4	no	—
149	C₄×C₃⋊D₃	M₁₆	1	4	yes	complemented
150	C₄×C₃⋊D₃	C₂×D₄	1	2	yes	—
151	C₄×C₃⋊D₃	#41	1	2	yes	—
152	C₃²×C₈	—	2	2	no	—
153	C₃²×C₈	—	2	1	no	—
154	C₃²×C₈	C₂×D₄	1	2	yes	complemented
155	C₃⋊(C₃⋊C₈)	—	2	2	no	—
156	C₃⋊(C₃⋊C₈)	—	2	1	no	—
157	C₃⋊(C₃⋊C₈)	C₂×D₄	1	2	yes	complemented
158	C₂²×M₁₆	—	9	2	no	—
159	C₂×C₄×D₄	—	9	1	no	—
160	#436	—	9	2	no	—
161	#436	—	9	1	no	—
162	#436	—	9	1	no	—
163	#436	—	9	2	no	—
164	#436	—	9	1	no	—
165	#436	C₃⋊D₃	1	1	yes	characteristic, direct product factor
166	C₂×C₄⋊C₈	—	9	1	no	—
167	C₂×C₂²⋊C₈	—	9	2	no	—
168	C₂×C₄×C₈	—	9	1	no	—
169	C₂³×D₃	—	3	8	no	—
170	C₂×C₃×D₄	C₄×D₃	1	4	yes	—
171	C₂²×C₃×C₄	C₂²×D₃	1	8	yes	—
172	C₂×#67	—	3	8	no	—
173	C₂²×Dic₃	—	3	8	no	—
174	D₃×D₄	—	6	16	no	—
175	C₂×D₁₂	—	3	4	no	—
176	C₂×C₄×D₃	—	3	4	no	—
177	C₂×C₄×D₃	—	3	4	no	—
178	C₂×C₄×D₃	—	3	4	no	—
179	C₂×C₄×D₃	—	3	8	no	—
180	C₂×C₄×D₃	—	3	8	no	—
181	C₂×C₄×D₃	—	3	8	no	—
182	C₂×C₄×D₃	—	6	16	no	—
183	C₂×C₄×D₃	—	6	16	no	—
184	C₃×M₁₆	—	2	16	no	—
185	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
186	C₂×C₃×C₈	C₂²×D₃	1	8	yes	—
187	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
188	C₃×C₄⋊C₄	C₄×D₃	1	4	yes	—
189	C₃×C₂²⋊C₄	C₄×D₃	1	8	yes	—
190	C₃×C₄²	C₂²×D₃	1	4	yes	—
191	#217	—	3	8	no	—
192	(C₂×D₃)⋊C₄	—	3	8	no	—
193	(C₂×D₃)⋊C₄	—	3	8	no	—
194	C₄⋊Dic₃	—	3	4	no	—
195	Dic₃⋊C₄	—	3	8	no	—
196	C₄×Dic₃	—	3	4	no	—
197	C₄×Dic₃	—	3	4	no	—
198	C₄×Dic₃	—	3	4	no	—
199	#208	—	6	16	no	—
200	C₂×C₃⋊C₈	—	3	4	no	—
201	C₂×C₃⋊C₈	—	3	4	no	—
202	C₂×C₃⋊C₈	—	3	8	no	—
203	ΓL(1,𝔽₂₅)	—	6	16	no	—
204	ΓL(1,𝔽₂₅)	—	6	16	no	—
205	D₃×C₈	—	3	16	no	—
206	D₃×C₈	—	6	16	no	—
207	D₃×C₈	—	6	8	no	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	2	no	—
210	C₂²×C₃²	—	2	2	no	—
211	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₃⋊D₃	—	2	2	no	—
213	C₂×C₃⋊D₃	—	2	2	no	—
214	C₂×C₃⋊D₃	—	2	2	no	—
215	C₂×C₃⋊D₃	—	4	8	no	—
216	C₂×C₃⋊D₃	C₄×D₄	1	2	yes	—
217	C₂×C₃⋊D₃	C₂×M₁₆	1	2	yes	—
218	C₂×C₃⋊D₃	#131	1	2	yes	—
219	C₃²×C₄	—	2	2	no	—
220	C₃²×C₄	—	2	1	no	—
221	C₃²×C₄	C₂×M₁₆	1	2	yes	complemented
222	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
223	C₃²×C₄	C₂×#41	1	1	yes	characteristic
224	C₃⋊Dic₃	—	2	2	no	—
225	C₃⋊Dic₃	—	2	1	no	—
226	C₃⋊Dic₃	C₄×D₄	1	2	yes	—
227	C₃⋊Dic₃	C₂×M₁₆	1	2	yes	complemented
228	C₂²×D₄	—	9	1	no	—
229	C₂³×C₄	—	9	2	no	—
230	C₂×M₁₆	—	9	2	no	—
231	C₂×M₁₆	—	9	2	no	—
232	C₂×M₁₆	—	9	2	no	—
233	C₂×M₁₆	—	18	8	no	—
234	C₂×M₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
235	C₂²×C₈	—	9	1	no	—
236	C₂²×C₈	—	9	2	no	—
237	C₂²×C₈	—	9	1	no	—
238	C₄×D₄	—	9	1	no	—
239	C₄×D₄	—	9	2	no	—
240	C₄×D₄	—	9	1	no	—
241	C₄×D₄	—	9	2	no	—
242	C₄×D₄	—	9	1	no	—
243	C₄×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	9	1	no	—
245	C₂×C₂²⋊C₄	—	9	2	no	—
246	C₂×C₄²	—	9	1	no	—
247	C₄⋊C₈	—	9	2	no	—
248	C₄⋊C₈	—	9	1	no	—
249	C₄⋊C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
250	C₂²⋊C₈	—	9	2	no	—
251	C₂²⋊C₈	—	9	2	no	—
252	C₂²⋊C₈	—	9	2	no	—
253	C₂²⋊C₈	C₂×C₃⋊D₃	1	2	yes	complemented
254	C₄×C₈	—	9	1	no	—
255	C₄×C₈	—	9	1	no	—
256	C₄×C₈	—	9	1	no	—
257	C₄×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
258	C₂³×C₃	C₂×C₄×D₃	1	8	yes	—
259	C₂²×D₃	—	3	4	no	—
260	C₂²×D₃	—	3	8	no	—
261	C₂²×D₃	—	6	16	no	—
262	C₂²×D₃	—	6	16	no	—
263	C₂²×D₃	—	6	16	no	—
264	C₃×D₄	—	2	8	no	—
265	C₂×C₃×C₄	—	2	8	no	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
268	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
269	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
270	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
271	#67	—	6	16	no	—
272	C₂×Dic₃	—	3	4	no	—
273	C₂×Dic₃	—	3	4	no	—
274	C₂×Dic₃	—	3	4	no	—
275	C₂×Dic₃	—	3	8	no	—
276	C₂×Dic₃	—	6	16	no	—
277	D₁₂	—	6	8	no	—
278	C₄×D₃	—	3	16	no	—
279	C₄×D₃	—	3	8	no	—
280	C₄×D₃	—	3	8	no	—
281	C₄×D₃	—	6	16	no	—
282	C₄×D₃	—	6	8	no	—
283	C₄×D₃	—	6	16	no	—
284	C₄×D₃	—	6	8	no	—
285	C₄×D₃	—	6	8	no	—
286	C₃×C₈	—	2	8	no	—
287	C₃×C₈	—	2	4	no	—
288	C₃×C₈	D₃×D₄	1	8	yes	complemented
289	C₃⋊C₈	—	3	8	no	—
290	C₃⋊C₈	—	6	8	no	—
291	C₃⋊C₈	—	6	4	no	—
292	C₂×C₃²	—	4	2	no	—
293	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
294	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
295	C₂×C₃²	C₂×#131	1	1	yes	characteristic
296	C₃⋊D₃	—	4	2	no	—
297	C₃⋊D₃	#436	1	4	yes	direct product factor
298	C₂⁴	—	9	2	no	—
299	C₂×D₄	—	9	2	no	—
300	C₂×D₄	—	9	1	no	—
301	C₂×D₄	—	18	4	no	—
302	C₂×D₄	C₄×C₃⋊D₃	1	1	yes	characteristic
303	C₂²×C₄	—	9	1	no	—
304	C₂²×C₄	—	9	1	no	—
305	C₂²×C₄	—	9	2	no	—
306	C₂²×C₄	—	9	2	no	—
307	C₂²×C₄	—	9	1	no	—
308	C₂²×C₄	—	9	2	no	—
309	C₂²×C₄	—	9	2	no	—
310	C₂²×C₄	—	18	4	no	—
311	C₂²×C₄	—	18	4	no	—
312	C₂²×C₄	C₂²×C₃⋊D₃	1	2	yes	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	18	4	no	—
315	M₁₆	—	18	4	no	—
316	M₁₆	—	18	4	no	—
317	C₂×C₈	—	9	1	no	—
318	C₂×C₈	—	9	4	no	—
319	C₂×C₈	—	9	1	no	—
320	C₂×C₈	—	9	2	no	—
321	C₂×C₈	—	18	4	no	—
322	C₂×C₈	—	18	2	no	—
323	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
324	C₂×C₈	C₂²×C₃⋊D₃	1	2	yes	—
325	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
326	C₄⋊C₄	—	9	2	no	—
327	C₄⋊C₄	—	9	1	no	—
328	C₄⋊C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
329	C₂²⋊C₄	—	9	2	no	—
330	C₂²⋊C₄	—	9	2	no	—
331	C₂²⋊C₄	—	9	2	no	—
332	C₂²⋊C₄	C₄×C₃⋊D₃	1	2	yes	—
333	C₄²	—	9	1	no	—
334	C₄²	—	9	1	no	—
335	C₄²	—	9	1	no	—
336	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
337	C₂²×C₃	—	2	8	no	—
338	C₂²×C₃	—	2	8	no	—
339	C₂²×C₃	—	2	8	no	—
340	C₂²×C₃	C₂²×C₄×D₃	1	4	yes	—
341	C₂×D₃	—	3	8	no	—
342	C₂×D₃	—	3	8	no	—
343	C₂×D₃	—	3	8	no	—
344	C₂×D₃	—	6	8	no	—
345	C₂×D₃	—	6	8	no	—
346	C₂×D₃	—	6	8	no	—
347	C₂×D₃	—	12	32	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	2	8	no	—
350	C₃×C₄	D₃×M₁₆	1	8	yes	complemented
351	C₃×C₄	C₂×D₃×D₄	1	4	yes	—
352	C₃×C₄	D₃×#41	1	4	yes	—
353	Dic₃	—	3	8	no	—
354	Dic₃	—	3	8	no	—
355	Dic₃	—	6	4	no	—
356	Dic₃	—	6	8	no	—
357	C₃²	C₂×#436	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	9	1	no	—
359	C₂³	—	9	2	no	—
360	C₂³	—	18	4	no	—
361	C₂³	—	18	4	no	—
362	C₂³	—	18	4	no	—
363	C₂³	C₂×C₄×C₃⋊D₃	1	2	yes	—
364	D₄	—	2	2	no	—
365	D₄	—	18	4	no	—
366	D₄	—	18	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	9	1	no	—
370	C₂×C₄	—	9	1	no	—
371	C₂×C₄	—	9	2	no	—
372	C₂×C₄	—	9	2	no	—
373	C₂×C₄	—	9	4	no	—
374	C₂×C₄	—	9	1	no	—
375	C₂×C₄	—	9	2	no	—
376	C₂×C₄	—	18	4	no	—
377	C₂×C₄	—	18	4	no	—
378	C₂×C₄	—	18	2	no	—
379	C₂×C₄	—	18	4	no	—
380	C₂×C₄	—	18	2	no	—
381	C₂×C₄	—	18	2	no	—
382	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
383	C₂×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
384	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
385	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	2	1	no	—
388	C₈	—	9	2	no	—
389	C₈	—	18	2	no	—
390	C₈	—	18	1	no	—
391	C₈	D₄×C₃⋊D₃	1	2	yes	complemented
392	C₂×C₃	—	4	8	no	—
393	C₂×C₃	C₄×D₃×D₄	1	4	yes	—
394	C₂×C₃	C₂×D₃×M₁₆	1	4	yes	—
395	C₂×C₃	D₃×#131	1	4	yes	—
396	D₃	—	3	16	no	—
397	D₃	—	12	8	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	9	2	no	—
402	C₂²	—	9	2	no	—
403	C₂²	—	9	2	no	—
404	C₂²	—	18	2	no	—
405	C₂²	—	18	2	no	—
406	C₂²	—	18	2	no	—
407	C₂²	—	36	8	no	—
408	C₂²	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	2	no	—
411	C₄	—	9	2	no	—
412	C₄	—	9	2	no	—
413	C₄	—	18	1	no	—
414	C₄	—	18	2	no	—
415	C₄	M₁₆×C₃⋊D₃	1	2	yes	complemented
416	C₄	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
417	C₄	#41×C₃⋊D₃	1	1	yes	characteristic
418	C₃	D₃×#436	1	4	yes	complemented
419	C₂	—	4	2	no	—
420	C₂	—	9	4	no	—
421	C₂	—	36	2	no	—
422	C₂	C₄×D₄×C₃⋊D₃	1	1	yes	characteristic
423	C₂	C₂×M₁₆×C₃⋊D₃	1	1	yes	characteristic
424	C₂	C₃⋊D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×C₃⋊D₃
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₃²×#436	C₂
prime radical	C₂×D₄×C₃⋊D₃	C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#436	C₃⋊D₃
hypocenter	C₃²	C₂×#436
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #436

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×M₁₆×C₃⋊D₃	C₂	semidirect
3. C₃²×#436	C₂	semidirect
4. #10592827	C₂	semidirect
5. #10592711	C₂	semidirect
6. #10592537	C₂	semidirect
7. C₃⋊D₃×C₄⋊C₈	C₂	semidirect
8. #10592428	C₂	semidirect
9. C₃⋊D₃×C₂²⋊C₈	C₂	semidirect
10. #10592387	C₂	semidirect
11. C₄×C₈×C₃⋊D₃	C₂	semidirect
15. C₂×C₃²×M₁₆	C₂²	semidirect
19. C₂×#3748	C₂²	semidirect
21. C₂×#3743	C₂²	semidirect
22. C₂×#3743	C₂²	semidirect
32. C₃²×C₄⋊C₈	C₂²	semidirect
33. C₃²×C₂²⋊C₈	C₂²	semidirect
34. C₃²×C₄×C₈	C₂²	semidirect
35. #63657	C₂²	semidirect
36. #63647	C₂²	semidirect
37. #63647	C₂²	semidirect
38. #63641	C₂²	semidirect
39. C₈×C₃⋊Dic₃	C₂²	semidirect
40. C₈×C₃⋊Dic₃	C₂²	semidirect
41. C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	semidirect
42. C₄×C₃⋊(C₃⋊C₈)	C₂²	semidirect
45. C₃×#436	D₃	semidirect
92. C₈×C₃⋊D₃	D₄	semidirect
96. C₂×C₃×M₁₆	C₂×D₃	semidirect
113. C₃×C₄⋊C₈	C₂×D₃	semidirect
114. C₃×C₂²⋊C₈	C₂×D₃	semidirect
115. C₃×C₄×C₈	C₂×D₃	semidirect
149. C₄×C₃⋊D₃	M₁₆	semidirect
154. C₃²×C₈	C₂×D₄	semidirect
157. C₃⋊(C₃⋊C₈)	C₂×D₄	semidirect
165. #436	C₃⋊D₃	direct (N × H)
221. C₃²×C₄	C₂×M₁₆	semidirect
227. C₃⋊Dic₃	C₂×M₁₆	semidirect
234. C₂×M₁₆	C₂×C₃⋊D₃	semidirect
249. C₄⋊C₈	C₂×C₃⋊D₃	semidirect
253. C₂²⋊C₈	C₂×C₃⋊D₃	semidirect
257. C₄×C₈	C₂×C₃⋊D₃	semidirect
288. C₃×C₈	D₃×D₄	semidirect
297. C₃⋊D₃	#436	direct (N × H)
350. C₃×C₄	D₃×M₁₆	semidirect
357. C₃²	C₂×#436	semidirect
391. C₈	D₄×C₃⋊D₃	semidirect
415. C₄	M₁₆×C₃⋊D₃	semidirect
418. C₃	D₃×#436	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×M₁₆×C₃⋊D₃	2
C₄×D₄×C₃⋊D₃	2
C₃²×#436	2
#10592827	2
#10592711	2
#10592537	2
C₃⋊D₃×C₄⋊C₈	2
#10592428	2
C₃⋊D₃×C₂²⋊C₈	2
#10592387	2
C₄×C₈×C₃⋊D₃	2
D₃×#436	3

Subgroups — C3⋊D3×#436 #11859254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#436 #11859254